Roton-vortex interactions in superfluid helium

Abstract

From a new mathematical identity and by using the fractional difference between the momentum of a roton and the momentum at the bottom of the roton minimum as a small expansion parameter, a first-order perturbation treatment of the roton-vortex interaction is developed. The resulting analytic expressions for the distribution of transverse momentum transfer, in terms of elliptic integrals, are shown to be in excellent agreement with recent computer-simulation results of Samuels and Donnelly and are convenient for computing the total momentum transfer.